Topic summary · Decision maths (D2)
Dynamic Programming summary
Dynamic programming builds an optimum from overlapping subproblems using stage–state tables.
Files: D2-Dynamic Programming.pdf · D2-Dynamic Programming answers.pdf · free public downloads · diagrams in the PDFs
Key learning points
- Define stages and states before filling numerical values.
- Reuse optimal sub-route costs (Bellman principle).
- Work systematically — often backwards from the end.
- Recover the policy by tracing the argmin/argmax decisions.
Worked example 1 — Memoisation
Why store the best cost to each state?
Working
That reuse is the core DP idea.
Worked example 2 — Define stages and states before filling numerical value
Use this method from the Dynamic Programming sheet: Define stages and states before filling numerical values.
Working
Each key learning point matches a question type on the printable worksheet.
Worked example 3 — Reuse optimal sub-route costs (Bellman principle)
Use this method from the Dynamic Programming sheet: Reuse optimal sub-route costs (Bellman principle).
Working
Each key learning point matches a question type on the printable worksheet.
Worked example 4 — Work systematically — often backwards from the end
Use this method from the Dynamic Programming sheet: Work systematically — often backwards from the end.
Working
Each key learning point matches a question type on the printable worksheet.
Worked example 5 — Recover the policy by tracing the argmin/argmax decisio
Use this method from the Dynamic Programming sheet: Recover the policy by tracing the argmin/argmax decisions.
Working
Each key learning point matches a question type on the printable worksheet.
Scaffolded Learning Sheet and answers (PDFs)
This page is a short, searchable overview for revision and search engines. Use the Scaffolded Learning Sheet first, then the Answers PDF for a full written solution. The printable PDFs remain the main classroom resource.